Transient pressure effects in the evolution equation for premixed flame fronts

A nonlinear evolution equation for a scalar field G(x, t) is derived, whose level surface G ₀=const. represents the interface of a thin premixed flame propagating in a flow field. The derivation is an extended version of an equation already proposed by Markstein 1]. It was reconsidered by Williams 2] as a basis for theoretical and numerical analysis and takes, in addition to flame curvature and flame stretch time variations of the bulk pressure, heat loss and nonconstant transport coefficients into account. The equation is an extension of earlier analyses where a flame evolution equation was derived for slightly wrinkled flames such that the front can be described by a single-valued function of a normal coordinate. That formulation excluded situations where the mean flame front has an arbitrary shape in space. Here the more general situation is analysed by using a two-length-scale asymptotic analysis. The leading-order solution of this analysis is equivalent to the equation originally derived by Markstein 1]. In addition to nonconstant properties and heat-loss effects, that had already been considered by Clavin and Nicoli 3], the influence of transient changes of the bulk pressure is analysed. All these effects are combined into a unified formulation which will serve as a basis for a new flamelet concept for premixed turbulent combustion.